The present invention relates generally to an electrical analog of a pumping system and more specifically to an improved device for measuring the phase relationship between two signals.
Installation or modification of natural gas or other fluid distribution systems requires consideration of a number of factors before work is undertaken. Variations in loads, distribution paths, pipe sizes and compressor speeds all have effects on the operation of the system as a whole. Compression waves created in the gas by the operation of reciprocating pumps and compressors are especially troublesome, as fluid acoustic resonances can be set up in the system. These resonances increase metal fatigue and shorten the life of joints, valves and other components of the system.
To assist in planning for control of pulsations and vibrations, an electrical analog of all fluid transfer components can be created. Present electrical systems analogize current to mass flow of the gas and voltage to pressure. Inductors, capacitors and resistors are used to model the mechanical properties of pipes and other components in the distribution system. A detailed model of a distribution system or sub-system can be set up and studied to predict the effects caused by changing various parameters in the operation of the system. Examples of the use of gas pumping system analogs are found in U.S. Pat. Nos. 2,951,638 and 2,979,940.
In order to utilize easily obtained components, the operating frequency of the electrical analog is typically substantially higher than that of the mechanical system. An electrical to mechanical frequency ratio describes this relationship, which can be in the neighborhood of 1,000 to 1. Component values and analog system parameters are chosen so that all events which occur during the operation of the model reflect events which will take place in a mechanical system. For example, the presence of an electrical resonance in the analog system at a certain frequency corresponds to an acoustical resonance at the corresponding mechanical speed.
One model of a reciprocating compressor or pump includes a capacitor which is driven by a sinusoidal voltage source. Due to inaccuracies in the use of a fixed capacitor to model the changing volume of a compressor cylinder, the driving signal must be shaped to insure that the electrical model gives accurate results. The amount of phase shift introduced into the driving signal by the shaping circuit is generally not accurately determinable.
To accurately model a multi-cylinder compressor, it is necessary that the driving signals into the various cylinders have a phase relationship equal to that of the mechanical system. When different cylinders are of different sizes, as is often the case, different wave shaping circuits must be employed, which makes phase measurements of the unshaped driving signal especially inappropriate.
At present, two methods are commonly used for determining the phase of each shaped signal relative to the reference signal. The first consists of measuring the phase difference between the unshaped driving signal and the reference signal with a conventional phasemeter. As mentioned above, this type of measurement is inaccurate for multi-cylinder compressors, where the subsequent phase shift may be different in the shaping circuit for each cylinder. A conventional phasemeter cannot be used directly on the shaped driving signal because the phase of the shaped signal cannot be determined from a zero crossing. Instead, it can only be determined from the positive peaks in the shaped signal, which correspond to the top-dead-center position of the mechanical piston.
A second method is the measurement of the pressure-time waveforms at the output of each model cylinder and a conventional phasemeter. This method is accurate only so long as the operating conditions on each cylinder are identical, which is rarely the case.
It would be desirable to have a phase indicating instrument which measures the phase relationship between a sinusoidal and a non-sinusoidal signal. With such an instrument, it would be possible to directly measure the phase between the reference signal and the shaped driving signal.